Solving Large-Scale Vehicle Routing Problems with Hybrid Quantum-Classical Decomposition

TL;DR

This paper introduces a hybrid quantum-classical decomposition method for large-scale vehicle routing problems, significantly reducing quantum resource requirements and demonstrating feasibility on complex instances.

Contribution

The paper proposes a two-level decomposition strategy combining problem and circuit-level techniques to enable quantum solutions for larger VRPs on near-term devices.

Findings

Achieved up to 95% circuit depth reduction

Reduced qubit count by 96%

Demonstrated feasibility on complex VRP instances

Abstract

We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm. A Problem-Level Decomposition partitions a 13-node (156-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further cut via Circuit-Level Decomposition, enabling execution on near-term quantum devices. Our approach achieves up to 95\% reductions in the circuit depth, 96\% reduction in the number of qubits and a 99.5\% reduction in the number of 2-qubit gates. We demonstrate this hybrid algorithm on the standard edge encoding of the VRP as well as a novel amplitude encoding. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.